Sometimes people think that they have answered a question but haven't really and then it appears on the front page or elsewhere in such a manner that no one else thinks to look at the question because it's already been answered (even if there is no accepted answer). It would be great to be able to flag an answer as unhelpful or that it didn’t' work and to then have it bubble up again o the front page and go back to red to show that there are no acceptable solutions on the question. This would also force people to do something about people’s responses as well as help users realize when there answer isn’t helpful. If there are no penalties to the poster then this just becomes a way to help them write better answers. You could even add a badge for really helpful people.
I believe that this is better than just looking for accepted answers as a ton of people don't ever check off acceptable answers and there are lots of junk answers as well. This way the user is required to check on the status of their question to keep it active.
I’d also suggest that this only results in a performance hit (if at all) for the person who posts the question. If I know that a person has checked the responses that people left and that the solutions were either unhelpful or wrong then I would be more likely to address the user’s problem